A track day is exactly the perfect place to try out your car; most people driving at them aren't racers.
I instruct at track days so I'll share the basics:
You'll need a helmet (Snell SA2010 or Snell SA2015) the club should be able to give you exact requirement.
So the basic weekend goes very much like autocross; you show up sign in and then go through a basic tech inspection.
As a newbie you'll be in a student group. On Saturday they'll do some class rooms sessions in the morning along with some skid pad style drills, then around lunch you'll likely do a couple of sighting laps at low speed so you can see where the corner statins are and where the track goes.In the afternoon your instructor will do the first two laps at a moderate pace, then you'll come into the pits swap seats so you can drive. You will likely have two on track sessions in the afternoon
On Sunday you'll do four sessions, you'll have an instructor for every session.
Sessions are usually 30 minutes long; broken out by skill and sped level. Student, novice, intermediate and expert.
There is a difference from track driving to autocross. The big difference is unlike autocross where the car responds immediately, the higher the speed the longer the car takes to respond, so you can't be near as aggressive.
As an instructor I focus on getting students to think about trajectory versus steering to hit your marks. I try to get people to make corrections by steering with the pedals (throttle steering & trail raking) rather than trying to make rapid steering inputs. Also remember on a road course you're trying to bend the tires slowly as to get them most out of all 4 tires at once. It's a different mindset from Autocross. Autocross of course will haven given you the car control skills as well as the ability to read the car quickly, so you'll have a huge leg up on most students.
I also, like most instructors, really really want you to have fun as well as progress.
My advice is go for it, you'll likely not be driving more than 75% of the cars capability but it will still be about 200% faster than you could on any on ramp or curvy mountain road.